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Title: The Supermodular Stochastic Ordering

Author(s): Margaret A Meyer and Bruno Strulovici

Publication Date: May 2013

Keyword(s): Concordance, Copula, Correlation, Interdependence, Majorization, Mixture, Supermodular and Tournament

Programme Area(s): Financial Economics, Industrial Organization and Public Economics

Abstract: In many economic applications involving comparisons of multivariate distributions, supermodularity of an objective function is a natural property for capturing a preference for greater interdependence. One multivariate distribution dominates another according to the `supermodular stochastic ordering' if it yields a higher expectation than the other for all supermodular objective functions. We prove that this ordering is equivalent to one distribution being derivable from another by a sequence of elementary, bivariate, interdependence-increasing transformations, and develop methods for determining whether such a sequence exists. For random vectors resulting from common and idiosyncratic shocks, we provide non-parametric sufficient conditions for supermodular dominance. Moreover, we characterize the orderings corresponding to supermodular objective functions that are also increasing or symmetric. We use the symmetric supermodular ordering to compare distributions generated by heterogeneous lotteries. Applications to welfare economics, committee decision-making, insurance, finance, and parameter estimation are discussed.

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Bibliographic Reference

Meyer, M and Strulovici, B. 2013. 'The Supermodular Stochastic Ordering'. London, Centre for Economic Policy Research. https://cepr.org/active/publications/discussion_papers/dp.php?dpno=9486